## Convex Analysis and Nonlinear Optimization: Theory and ExamplesOptimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained. |

### From inside the book

Results 1-5 of 64

Theory and Examples Jonathan M. Borwein, Adrian S. Lewis. Ouvrages

demathématiques dela SMC 1 HERMAN/KUCERA/SIMSA Equations and

Inequalities 2 ARNOLD Abelian Groups and Representations of

**Finite**Partially

Ordered Sets 3 ...

Good reference works on

**finite**-dimensional convex analysis already exist.

Rockafellar's classic Convex Analysis (149) has been indispensable and

ubiquitous since the 1970s, and a more general sequel with Wets, Variational

Analysis [150], ...

However, rather like Halmos's

**Finite**Dimensional Vector Spaces [81], ease of

extension beyond

**finite**dimensions substantially motivates our choice of

approach. Where possible, we have chosen a proof technique permitting those

readers ...

... Brouwer Fixed Point Theorem . . . . . . . . . . . . . . 179 8.2 Selection and the

Kakutani—Fan Fixed Point Theorem . . . 190 8.3 Variational Inequalities . . . . . . . .

. . . . . . . . . . . . . 200 9 Postscript: Infinite Versus

**Finite**Dimensions 209 9.1

Introduction .

Our setting, for most of the book, is an arbitrary Euclidean space E, by which we

mean a

**finite**-dimensional vector space over the reals R, equipped with an inner

product (, ). We would lose no generality if we considered only the space R” of ...

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### Contents

15 | |

Fenchel Duality | 33 |

Convex Analysis | 65 |

Special Cases | 97 |

Nonsmooth Optimization | 123 |

KarushKuhnTucker Theory | 153 |

Fixed Points | 179 |

Infinite Versus Finite Dimensions | 209 |

List of Results and Notation | 221 |

Bibliography | 241 |

Index | 253 |

### Other editions - View all

Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis No preview available - 2000 |